Preheat oven to 400ºF.
- Press pie crust into pie pan; flute edges.
- Combine sugar, pumpkin pie spice and corn starch in a large bowl.
Peel and core apples; cut into ¼-inch thick slices and place in a separate bowl.
- Sprinkle apples with lemon juice and rum; add to dry ingredients.
- Stir to combine.
- Place in pie crust.
- Dot with 2 tablespoons of butter.
- Drizzle with caramel sauce.
- Stir flour and brown sugar together in small bowl.
Cut in ¼ cup butter until mixture resembles coarse meal.
- Sprinkle evenly over top of pie.
- Bake 10 minutes.
Reduce heat to 350ºF and bake an additional 40 to 50 minutes, until golden brown.
- Serve warm with vanilla ice cream, if desired.